objectives finish with heat transfer learn about psychometrics psychometric chart
TRANSCRIPT
Objectives
Finish with Heat transfer
Learn about Psychometrics• Psychometric chart
Forced Convection
• External turbulent flow over a flat plate• Nu = hmL/k = 0.036 (Pr )0.43 (ReL
0.8 – 9200 ) (µ∞ /µw )0.25
• External turbulent flow (40 < ReD <105) around a single cylinder• Nu = hmD/k = (0.4 ReD
0.5 + 0.06 ReD(2/3) ) (Pr )0.4 (µ∞ /µw )0.25
• Use with careReL = Reynolds number based on length Q = heat transfer rate (W, Btu/hr)
ReD = Reynolds number based on tube diameter A = area (m2, ft2)
L = tube length (m, ft) t = temperature (°C, °F)
k = thermal conductivity (W/m/K, Btu/hr/ft/K) Pr = Prandtl numberµ∞ = dynamic viscosity in free stream( kg/m/s, lbm/ft/min)
µ∞ = dynamic viscosity at wall temperature ( kg/m/s, lbm/ft/min)
hm = mean convection heat transfer coefficient (W/m2/K, Btu/hr/ft2/F)
Natural Convection
• Common regime when buoyancy is dominant• Dimensionless parameter• Rayleigh number
• Ratio of diffusive to advective time scales
• Book has empirical relations for • Vertical flat plates (eqns. 2.55, 2.56)
• Horizontal cylinder (eqns. 2.57, 2.58)
• Spheres (eqns. 2.59)
• Cavities (eqns. 2.60)
Pr
TgHTHgRa
/T 2
33
H = plate height (m, ft)T = temperature (°C, °F)
Q = heat transfer rate (W, Btu/hr)
g = acceleration due to gravity (m/s2, ft/min2)
T = absolute temperature (K, °R)
Pr = Prandtl number
ν = kinematic viscosity = µ/ρ (m2/s, ft2/min)
α = thermal diffusivity (m2/s)
Phase Change –Boiling
• What temperature does water boil under ideal conditions?
Radiation
• Transfer of energy by electromagnetic radiation• Does not require matter (only requires that the
bodies can “see” each other)• 100 – 10,000 nm (mostly IR)
Surface Radiation Issues
1) Surface properties are spectral, f(λ)
Usually: assume integrated properties for two beams:
Short-wave and Long-wave radiation
2) Surface properties are directional, f(θ)
Usually assume diffuse
Radiation emission The total energy emitted by a body,
regardless of the wavelengths, is given by:
Temperature always in K ! - absolute temperatures
– emissivity of surface ε= 1 for blackbody
– Stefan-Boltzmann constant
A - area
4ATQemited
Short-wave & long-wave radiation
• Short-wave – solar radiation• <3m• Glass is transparent • Does not depend on surface temperature
• Long-wave – surface or temperature radiation• >3m• Glass is not transparent • Depends on surface temperature
Radiation Equations
2
2
2
1
211
1
42
411
21111
)(
AA
F
TTAQ
2
2
2
1
211
1
3
2
2
2
1
211
1
21
42
41
111
4
111
)()(
AA
F
T
AA
F
TTTT
havg
r
tAhQ rrad
Q1-2 = Qrad = heat transferred by radiation (W, BTU/hr) F1-2 = shape factor
hr = radiation heat transfer coefficient (W/m2/K, Btu/hr/ft2/F) A = area (ft2, m2)
T,t = absolute temperature (°R , K) , temperature (°F, °C)
ε = emissivity (surface property)σ = Stephan-Boltzman constant = 5.67 × 10-8 W/m2/K4
= 0.1713 × 10-8 BTU/hr/ft2/°R4
Combining Convection and Radiation
• Both happen simultaneously on a surface• Slightly different
temperatures
• Often can use h = hc + hr
Humidity Ratio, W
• W = mw/ma
• Degree of saturation, µ = W/Ws
• Humidity ratio is hard to measure, but very useful in calculations
• What are units?
• Is W a function of temperature? What about Ws?
Ws = humidity ratio at saturationma = mass of dry airmw = mass of water vapor
Relative Humidity
• Φ = xw/xw,s = Pw/Pws
• Function of T
Easy to measure and useful in some contexts, but often need to know temperature as well
W
Ws
622.0
622.0
x = mole fractionP = pressureμ = degree of saturationW = humidity ratio
Dew-point temperature, td
• Temperature at which condensation will form• Under appropriate surface conditions
• Vapor is saturated
• Φ = ?
• Ws(P, td) = W
Wet-bulb temperature, VBT (t*)
• Temperature of wet surface or
• Temperature at which water, by evaporating into the air, will bring air to saturation adiabatically
• * superscript is designation that variable is evaluated at the wet-bulb temperature
• Note, distinct from that measured by a sling psychrometer• Section 9.5
Tables for Moist Air (P = 1 atm)
• Tables A.4 in your text
• Ability to get Ws for calculations
• Subscripts:• a = dry air, s = saturated air
v = va+µvas
h = ha+µhas
s = sa+µsas
Psychrometric Chart
• Need two quantities for a state point• Can get all other quantities from a state point
• Can do all calculations without a chart• Often require iteration• Many “digital” psychrometric charts available
• Can make your own
• Best source is ASHRAE fundamentals (Chapter 6)• Also in your text (back cover fold-out)
Ref: Tao and Janis (2001)
Ref: Tao and Janis (2001)
Ref: Tao and Janis (2001)
Ref: Tao and Janis (2001)
Examples
• What is enthalpy of air in the classroom right now?
• Condensation on windows when taking a shower
• How cold does it have to be outside for condensation to form on windows?
– Assumption is that windows are the same temperature as outside air
– 80 °F, RH = 80%
Alternate calculation for W
• PV = mRT (IGL)
• What do we know about R ratio?
• P = Pw + Pa
w
a
a
w
TRVP
TRVP
a
w
R
R
P
P
m
mW
a
a
w
w
w
w
PP
PW
622.0
R = gas constantP = pressureV = volumeT = absolute temperatureW = humidity ratio
Subscripts: w is water vapor, a is dry air
Calculation of psychometric quantities
• For an ideal gas,• hda = ∫cpadT, hw = ∫cpwdT
• So, hda = cp,dat which assumes a reference state of 0 °F or 0 °C – Tables A4• Note different reference
• hw = cpwt + hg0
• h = cp,dat + W(cpwt + hg0)Or you can use:• h = cpt + W∙hg0, cp = cp,da + Wcpw
cp = specific heath = enthalpyT = absolute temperaturet = temperature W = humidity ratio
Subscripts: w is water vapor, a is dry air, g is saturated water vapor
Adiabatic mixing
• Governing equation hmQhmoutin
External heat
Sensible heating
tcmQ p
Dehumidification by Cooling
Real Dehumidification Process
Mold in a duct
Transport of saturated air
tsurface < tdp Condensation
Humidification
hw Specific enthalpy of water added to system
hg Specific enthalpy of saturated water vapor
Summary
• Describe psychrometric quantities
• Given any two psychrometric quantities, calculate any other quantity
• Use Tables A4 or psychrometric charts to look up psychrometric quantities
• Calculate psychrometric quantities at non-standard conditions